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Cooperative Clustering in Transportation Network Optimization

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  • 1. Cooperative-Based Clustering in Transportation Network Optimization May 8, 2014 1 Introduction A promising approach on transportation network optimization that combines the strengths of various clustering algorithms is introduced. The main idea of this approach was inherited from document clustering but has been modied for use on graph data. 1.1 Transportation Network Optimization (TNO) A transportation network is a dynamic, stochastic, and complex system. Mod- eled as a graph, nodes fall into categories that correspond to manufacturing sources, distribution centers, and end customers. The most common objective in transportation network optimization is to nd the shortest-distance distribution on a network, i.e., to determine an opti- mal set of routes between suppliers and customers. Today there is a growing interest in a new and much more sophisticated class of network solutions that involve multiple optimization factors like prot, service level, fault tolerance (or resilience), and environmental footprint, with the optimal solution balancing the complex trade-os among all these parameters simultaneously. 1.2 Cluster Analysis in TNO Designing a distribution network often involves planning of routes over regions or deciding on locations for warehouses. Cluster analysis oers an alternative solution to categorize locations in a systematic way and speeds up the process of exploring several dierent versions of the clusters. Although clustering algorithms have been successfully applied in specic transportation network optimization problems, but the question of how can we identify the clustering algorithm best suited for a particular problem remains unanswered. My hypothesis is that an ensemble approach that synthesizes a solution from the results of an aggregation of constituent clustering algorithms, with multiple optimization factors like prot, service level, fault tolerance (or resilience), and environmental footprint, will produce measurably better results 1
  • 2. Extracting Program Structure CC/G {Ca1 ….. Cam} {Cb1 ….. Cbm} {Cd1 ….. Cdm} {Ce1 ….. Cem} Clusters Set CC/G Clusters graph structure inherent in software Software Program1 Software Programn Structure Partitioning • Hill Climbing (with three different configurations) • Lattix Partitioning Algorithm Evaluation • Partitioning Quality • Similarity Figure 1: Data ow diagram for cooperative based clustering in software archi- tecture recovery than any one of those algorithms individually. This approach has been explored in various disciplines, but according to our knowledge no work has been done for transportation network optimization. 1.3 Cooperative Based Clustering Cooperative Clustering on Graphs is an unsupervised learning algorithm for clustering a graph networks into k partitions based on intra-cluster density and inter-cluster sparsity. The main idea is to apply dierent clustering algorithms on the graph network. Each algorithm will provide dierent k clusters. A com- mon agreement among those clusterings is then found. This agreement identies the minimum number of k clusters that the graph network should have. The last step is to merge the remaining graph elements that exhibited disagreement in- between the clusters that were initially determined using optimum intra-cluster density and inter-cluster sparsity. These steps are illustrated by gure 1. Figure 1 has been adopted from a recent published paper in the software engineering domain [2]. Relevant Publication 1. A. Ogunbanwo, A. Williamson, M. Veluscek, R. Izsak, T. Kalganova, P. Broomhead (2013), Transportation Network Optimization, Encyclopedia of Business Analytics and Optimization. 2. A. Ibrahim, D. Rayside, R. Kashef, Cooperative Based Software Clus- tering on Dependency Graphs, IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), Toronto, Canada (May, 2014). 3. R. Naseem, O. Maqbool, and S. Muhammad, Cooperative clustering for software modularization, Journal of Systems and Software, 2013. 2
  • 3. 4. Rasha Kashef and Mohamed S. Kamel, Cooperative clustering,Pattern Recognition, vol. 43, no. 6, pp. 2315 2329, 2010. 5. William Eberle and Lawrence Holder. Anomaly Detection in Data Rep- resented as Graphs. Intelligent Data Analysis: An International Journal. Volume 11, Number 6, pp. 663-689. 2007 3